Listen to top Democrats and Republicans talk on camera, and it sounds like they could not be further apart on a year-end tax-and-spending deal – a down payment on a $4 trillion grand bargain.

But behind the scenes, top officials who have been involved in the talks for many months say the contours of a deal – including the size of tax hikes and spending cuts it will likely contain — are starting to take shape.

Cut through the fog, and here’s what to expect: Taxes will go up just shy of $1.2 trillion — the middle ground of what President Barack Obama wants and what Republicans say they could stomach. Entitlement programs, mainly Medicare, will be cut by no less than $400 billion - and perhaps a lot more, to get Republicans to swallow those tax hikes. There will be at least $1.2 trillion in spending cuts and “war savings.” And any final deal will come not by a group effort but in a private deal between two men: Obama and House Speaker John Boehner (R-Ohio). The two men had what one insider described as a short, curt conversation Wednesday night — but the private lines of communications remain very much open.

No doubt, there will be lots of huffing and puffing before any deal can be had. And, no doubt, Obama and Congress could easily botch any or all three of the white-knuckle moments soon to hit this town: the automatic spending cuts and expiration of the Bush tax cuts, both of which kick in at the end of this year, and the federal debt limit that hits early next.

But it’s clear to veterans of this budget fight a deal is there to be done. Here is the state of play that is sketched out by top officials in both parties:

The coming tax hike

There is no chance taxes are not going up for people making north of $250,000 – and virtually no chance that doesn’t include their tax rates, too.

Republicans publicly say they are opposed to rate hikes – but privately they know they are going up, if not all the way to the Clinton-era 39.6 percent, then darn close.

The reason is simple math. Take a look at this list, and you will see that any tax loopholes worth closing won’t get Obama or Republicans close to their targets.

To those involved in the talks, it’s not really a mystery how big the overall hike will be. Boehner was for $800 billion before the election, and Obama slapped down an opening bid of $1.6 trillion after. So it doesn’t take Ernst and Young to add those numbers, divide by two and know the president wants to end up close to $1.2 trillion.

House Republicans, already worried about possible primary challenges in 2014, are pleading to keep that number below $1 trillion, even if it is by a hair. Still, they know it’s likely to come in a shade higher. The safe bet is just over $1 trillion for the final number. A bit less, and that’s a notable win for Boehner.

Officials familiar with the White House position say Obama plans zero flexibility on his insistence on a higher tax rate for top earners. He plans to take what one aide called a “trust but verify” position: He will insist on a higher rate in the year-end deal. Then next year, during tax-reform negotiations, “the onus will be on Republicans to propose something that raises the same amount of revenue,” the aide said. “He’s going to pocket their rate hike on the top two brackets at first, and then he’s going to say to them in the 2013 process that we set up: If you think you can realize these same revenues in a different way, prove it to me.”

A rate hike would be the most difficult element for Boehner to sell to his own members. But Republicans are already trying to build the case — both with their own members and with constituents — that whatever the final deal, they fought hard. And the Speaker has drawn a sharp distinction between increasing revenue, which he will accept, and raising rates, which he has said he will not. Kevin Smith, Boehner’s communications director said: “We have no intention of increasing tax rates. Doing so will hurt small business and destroy jobs.”

John Boehner to GOP: Stick together on taxes

Boehner told his conference in a closed-door meeting Wednesday morning: “We’ve staked out a principled position. It’s important that everyone in this room continue to be clear with our constituents about what that position is: We’re fighting for spending cuts. We’re fighting against increases in tax rates that destroy jobs. And we’re fighting for pro-growth tax reform and entitlement reform, the keys to economic growth.” And the Speaker narrated slides from Republican pollster David Winston arguing that most Americans prefer overall tax reform to higher rates for the rich.

So what does the final tax hike look like? That will take a while to hash out but those involved guess it will include a rate hike, higher taxes on carried interest and probably capital gains and dividends, and either a cap on total deductions for rich people or some form of a minimum tax rate for them.

The coming entitlement cuts

There is only way to make the medicine of tax hikes go down easier for Republicans: specific cuts to entitlement spending. Democrats involved in the process said the chest-pounding by liberals is just that – they know they will ultimately cave and trim entitlements to get a deal done.

A top Democratic official said talks have stalled on this question since Obama and congressional leaders had their friendly looking post-election session at the White House. “Republicans want the president to own the whole offer upfront, on both the entitlement and the revenue side, and that’s not going to happen because the president is not going to negotiate with himself,” the official said. “There’s a standoff, and the staff hasn’t gotten anywhere. Rob Nabors [the White House negotiator], has been saying: ‘This is what we want on revenues on the down payment. What’s you guys’ ask on the entitlement side?’ And they keep looking back at us and saying: ‘We want you to come up with that and pitch us.’ That’s not going to happen.”

Sen. Dick Durbin (D-Ill.) told “Morning Joe” on Tuesday that he could see $400 billion in entitlement cuts. That’s the floor, according to Democratic aides, and it could go higher in the final give and take. The vast majority of the savings, and perhaps all of it, will come from Medicare, through a combination of means-testing, raising the retirement age and other “efficiencies” to be named later. It is possible Social Security gets tossed into the mix, but Senate Majority Leader Harry Reid (D-Nev.) plans to fight that, if he has to yield on other spending fronts.

Democrats want most Medicare and other entitlement savings to kick in between 10 and 20 years from now, which will make some Republicans choke. Democrats will point to the precedent set by House Budget Chairman Paul Ryan (R-Wis.) of pushing most mandatory savings off until a decade from now.

“A lot of the big entitlement savings comes in the 10-20 year budget window, not the next 10 years,” a Democratic aide said. “Everybody will need to get on board understanding that. Paul Ryan and the Obama budget are the same on health cuts for next 10 years.”

But that will likely be the deal Republicans will be staring at: tax hikes now in exchange for Medicare changes way later. That will require some fancy footwork by Boehner to sell.

The coming cave

People who have talked privately with the top three House Republican leaders — Boehner, House Majority Leader Eric Cantor (R-Va.) and House Majority Whip Kevin McCarthy (R-Calif.) – say they recognize that Obama holds the high cards, and that the public is likely to blame Republicans if negotiations blow up and the new year brings a fiscal disaster. Ryan, back at the Capitol after spending the fall on the road as Mitt Romney’s running mate, is said to be resisting concessions that the others consider inevitable.

Ryan, who is considering a run for president, will ultimately have to decide if he wants to be party to a deal - or if he wants to be the public leader of the resistance.

If that happens, Cantor becomes all the more important to getting a final deal through the House. Cantor is a bigger player than some think and his relationship with Boehner is stronger today than six months ago. The staff-level tension, which was often a distraction for both men, has abated ever since Barry Jackson left as Boehner’s top aide. Cantor, who is better versed on the details of tax issues than most members of Congress, also remains relatively tight with Vice President Joe Biden, a relationship that Bob Woodward’s book, “The Price of Politics,” revealed to be closer and more important than commonly known.

A Pew Research Center poll this month had sobering figures for Republicans: 53 percent of respondents said the GOP would be more to blame if the country goes over the fiscal cliff, while only 29 percent said Obama. A CNN/ORC poll this week had a similar finding: 45-34.

Even Grover Norquist, president of Americans for Tax Reform, sounded more pragmatic than doctrinaire during a Playbook Breakfast interview on Wednesday. He said that while Republicans need to avoid having “their fingerprints on the murder weapon” of a tax increase, they will have a defensible position if negotiations are conducted in public, they push for reforms, and the deal can “pass the laugh test” back home. That leaves a lot of leeway.

Spending cuts will be crucial to this. The floor for new spending cuts is simple: replacing the $1.2 trillion in automatic cuts set to kick in if the two parties can‘t cut a deal before year’s end. Republicans will insist these are real and imminent to swallow the rest.

It’s the Obama-Boehner show

Everyone has an opinion on the grand bargain. But only two matter: Obama’s and Boehner’s. Any deal will ultimately be hammered out between the two men, whose on-again, off-again relationship is stronger than most people realize.

Bluster aside, both know they have a heavy incentive to cut a deal, and quick. Boehner knows the president isn’t bluffing on letting the Bush tax cuts lapse to get his way on raising rates on the rich. Obama knows the last thing he wants at the start of a second term is an economic funk caused by Washington dysfunction, even if Republicans get more of the blame.

People involved in the talks over the past six months say House Minority Leader Nancy Pelosi is at best a bit player in the unfolding drama, and virtually certain to back any deal Obama blesses. Reid runs the Senate and has more juice than Pelosi, but he knows his role is to play bad cop until it’s time play loyal soldier to pass the final package. Senate Minority Leader Mitch McConnell, facing a reelection two years from now in conservative Kentucky, will defer to Boehner in brokering any compromise and might even break with his fellow GOP leader on a final vote.